Optimal energy decay rate of coupled wave equations

Ahmed Benaddi

Abstract: We consider a system of coupled wave equations subject to positive viscous damping. Under the assumption that the damping function is of bounded variations, we give the asymptotic expansion of eigenvalues and eigenfunctions of the infinitesimal generator of the associated semigroup. Moreover, we prove that the eigenfunctions form a Riesz basis in the energy space.

Keywords: viscous damping; asymptotic expansion of the eigenvalues; Riesz basis; optimal decay rate.

Classification (MSC2000): 35C20, 35P20, 35P10, 93D15.

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